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Expression of type Conditional

from the theory of proveit.logic.booleans.implication

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional
from proveit.logic import And, Boolean, Implies, InSet, Not
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Implies(A, B), And(Implies(Not(B), Not(A)), InSet(B, Boolean)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{A \Rightarrow B \textrm{ if } (\lnot B) \Rightarrow (\lnot A) ,  B \in \mathbb{B}\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 8
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple19, 18
4Literal
5ExprTuple6, 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple18, 14
12Operationoperator: 16
operand: 18
13Operationoperator: 16
operand: 19
14Literal
15ExprTuple18
16Literal
17ExprTuple19
18Variable
19Variable